I feel like this is going to be a warranty nightmare. Anyone with kids can tell you this will 100% break. Additionally, that controller is going to add weight, as well as limit internal space available for battery and thermal design. I imagine that this thing is going to be riddled with issues. Not to mention it'll be crazy expensive.
The other issue here is game compatibility and button mapping. It's reliance on one more piece of software and driver to be compatible with Steam or whatever gaming platform you're using. And if this laptop bombs, you can say goodbye to any updates or support in the future.
Are people really that averse to simply bringing an XBox controller with them? Or if that takes up too much space, grab an 8bitdo.